A304690 Primes p > 5 such that no polygonal number P_s(k) (with s >= 3, k >= 5 ) is equal to p - 1.

7, 11, 13, 17, 19, 23, 31, 41, 43, 47, 53, 59, 61, 73, 83, 89, 103, 107, 109, 131, 139, 151, 163, 167, 173, 179, 181, 193, 199, 223, 227, 229, 241, 251, 263, 269, 271, 283, 293, 311, 313, 347, 349, 353, 359, 383, 389, 419, 421, 431, 433, 439, 443, 463, 467, 479, 499, 503, 509, 521, 523, 557, 563, 571, 587, 593, 599

Offset

1,1

Comments

For all primes p > 5, at least one polygonal number exists with P_s(k) = p - 1 when k = 3 or 4, dependent on p mod 6; this is why the sequence is defined for k >= 5.

Set of primes without {A304688} and {2,3,5}.

Links

Table of n, a(n) for n=1..67.

OEIS, Nontrivial polygonal numbers

Mathematica

lst = {}; Do[
If[! Resolve[
    Exists[{s, k},
     Prime[m] == 1/2 k (4 + k (-2 + s) - s) + 1 && s >= 3 && k >= 5],
    Integers], lst = Union[lst, {Prime[m]}]], {m, 4, 150}]; lst

Crossrefs

Cf. A000040, A304688.

Sequence in context: A028416 A040121 A156114 * A091554 A111980 A108811

Adjacent sequences: A304687 A304688 A304689 * A304691 A304692 A304693

Keyword

nonn

Author

Ralf Steiner, May 17 2018

Status

approved